First, you need to sign in using Twitter. After that, you can confirm if you want to do this and continue or cancel the wipe.
About signing in: TwitWipe uses safe oAuth authentication, so you don't need to give out your password for this to happen. If you're signed into Twitter, this will directly ask you for permissions. If you're not signed in, it will take you to Twitter.com and ask you to sign in to proceed. As usual, check that the website URL in the location bar is indeed "twitter.com" and the padlock or security icon is present before typing your password in!
Please solve the following puzzle to prevent automated/bot usage: